Correction method for image forming apparatus

ABSTRACT

A correction method for an image forming apparatus including a light source including a plurality of light emitting points, a photosensitive member configured to rotate in a first direction, and a deflection unit configured to deflect light beams emitted from the light source in a second direction orthogonal to the first direction to form scanning lines, the correction method including: a storing step of storing information on positional deviation of the scanning lines in the first direction; a conversion step of converting positions of pixels of an input image by performing coordinate transformation based on the information so that an interval of the scanning lines becomes a predetermined interval; and a filtering step of determining pixel values of pixels of an output image by subjecting pixel values of the pixels of the input image after the coordinate transformation to a convolution operation.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to a correction method for an imageforming apparatus, for correcting distortion and uneven image density ofan image during image formation of a two-dimensional image by the imageforming apparatus, e.g., a digital copying machine, a multifunctionalperipheral, or a laser printer.

Description of the Related Art

In electrophotographic image forming apparatus such as a laser printerand a copying machine, there has been generally known a configuration toform a latent image on a photosensitive member with use of a lightscanning device configured to perform scanning with a laser beam. In thelight scanning device of a laser scanning type, a laser beam collimatedwith use of a collimator lens is deflected by a rotary polygon mirror,and the deflected laser beam is formed into an image on a photosensitivemember with use of an elongated fθ lens. Further, there is knownmultibeam scanning in which a laser light source having a plurality oflight emitting points is included in one package so as to performscanning with a plurality of laser beams simultaneously.

Meanwhile, in order to form a satisfactory image without uneven imagedensity and banding, it is desired that distances between scanning linesof which positions to be scanned with a laser beam are adjacent to eachother in a rotational direction of the photosensitive member be equal toeach other. However, the distances between the scanning lines are varieddue to a plurality of factors described below. The distances between thescanning lines on the photosensitive member are varied by, for example,a fluctuation in a surface speed of the photosensitive member, or arotation speed fluctuation of a rotary polygon mirror. Further, thedistances between the scanning lines are also varied by a variation inangle of mirror faces of the rotary polygon mirror with respect to arotary shaft of the rotary polygon mirror and a variation in intervalsbetween light emitting points arranged on a laser light source. FIG. 16Ais an illustration of a state in which an interval between the scanninglines is varied periodically, with scanning of laser beams beingrepresented by horizontal lines. As illustrated in FIG. 16A, when theinterval between the scanning lines of laser beams is small, an image isdeveloped darkly. When the interval between the scanning lines of laserbeams is large, an image is developed lightly. Thus, this development isliable to be detected as moire and the like. To cope with uneven imagedensity and banding caused by such factors, there has been proposed atechnology of correcting banding by controlling an exposure amount ofthe light scanning device. For example, in Japanese Patent ApplicationLaid-Open No. 2012-098622, there is described a configuration in which abeam position detection unit configured to detect a beam position in asub-scanning direction is arranged in the vicinity of the photosensitivemember, and the exposure amount of the light scanning device is adjustedbased on scanning distance information obtained from a detected beamposition, to thereby make banding less noticeable.

However, in the conventional method of adjusting density based on theexposure amount, an optimum amount of controlling a light amount isvaried depending on a change in image forming conditions of the imageforming apparatus. Therefore, it is difficult to perform bandingcorrection stably. As the changes in image forming conditions, there aregiven, for example, a change in ambient temperature environment of theimage forming apparatus, a change in sensitivity to light of thephotosensitive member, and a change with time of characteristics of atoner material.

Further, in a color image forming apparatus, when positional deviationoccurs at a relatively long period, positional deviation occurs betweencolors at a long period to cause an image defect, e.g., uneven hue. FIG.16B is an illustration of a state of positional deviation of eachscanning line. When printing is performed at a resolution of 1,200 dpi(scanning line interval: 21.16 μm) with respect to an image having animage width of 297 mm in an A4 longitudinal direction, about 14,000scanning lines are formed. Due to the above-mentioned factors, e.g., afluctuation in surface speed of the photosensitive member, thepositional deviation amount between an ideal position of the scanningline and an actual scanning position in an image area is varied in anon-uniform manner. In FIG. 16B, in the 2,000th line and 7,000th linefrom a leading edge of an image, the scanning position of a scanningline represented by the solid line is deviated in a front direction froman ideal position represented by the broken line, and in the 10,000thline, the scanning position is deviated in a direction opposite to thefront direction. Thus, when the scanning line, that is, the imageposition is deviated from the ideal position in the image area, aproblem, e.g., a hue variation occurs, and hence a configuration to movethe absolute position of image data is required.

SUMMARY OF THE INVENTION

The present invention has been made under the above-mentionedcircumstances, and it is an object of the present invention to obtainsatisfactory image quality by correcting uneven image density of animage, which occurs in a direction corresponding to a rotationaldirection of a photosensitive member.

According to one embodiment of the present invention, there is provideda correction method for an image forming apparatus, the image formingapparatus comprising: a light source comprising a plurality of lightemitting points; a photosensitive member configured to rotate in a firstdirection so that a latent image is formed on the photosensitive memberwith light beams emitted from the light source; and a deflection unitconfigured to deflect the light beams emitted from the light source tomove spots of the light beams radiated to the photosensitive member in asecond direction orthogonal to the first direction to form scanninglines, the correction method comprising: a storing step of storing, in astorage unit, information on positional deviation of the scanning linesin the first direction; a conversion step of converting positions ofpixels of an input image by performing coordinate transformation basedon the information stored in the storage unit so that an intervalbetween the scanning lines on the photosensitive member becomes apredetermined interval; and a filtering step of determining pixel valuesof pixels of an output image by subjecting pixel values of the pixels ofthe input image to a convolution operation based on the positions of thepixels of the input image after the coordinate transformation.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a view for illustrating an entire image forming apparatusaccording to first and second embodiments.

FIG. 1B is a view for illustrating a configuration of the periphery of aphotosensitive drum and a light scanning device.

FIG. 2 is a block diagram of the image forming apparatus according tothe first and second embodiments.

FIG. 3 is a diagram for illustrating positional deviation of scanninglines according to the first embodiment.

FIG. 4 is a block diagram for illustrating a step of storing informationin a memory according to the first embodiment.

FIG. 5 is a flowchart for illustrating correction processing accordingto the first embodiment.

FIG. 6A, FIG. 6B, FIG. 6C, and FIG. 6D are each a diagram forillustrating positional deviation of pixels for each classificationaccording to the first embodiment.

FIG. 7A and FIG. 7B are each a graph for showing coordinatetransformation of pixel positions in a sub-scanning direction accordingto the first embodiment.

FIG. 8A, FIG. 8B, FIG. 8C, and FIG. 8D are each a graph for showingcoordinate transformation of pixel positions in the sub-scanningdirection according to the first embodiment.

FIG. 9A and FIG. 9B are each a graph for showing coordinatetransformation of pixel positions in the sub-scanning directionaccording to the first embodiment.

FIG. 10A, FIG. 10B, and FIG. 10C are each a graph for showing aconvolution function to be used in filtering according to the firstembodiment.

FIG. 10D is a graph for showing a correction value and a coefficient.

FIG. 11A, FIG. 11B, FIG. 11C, and FIG. 11D are each a diagram forillustrating the filtering for each classification of positionaldeviation according to the first embodiment.

FIG. 12 is a flowchart for illustrating the filtering according to thefirst embodiment.

FIG. 13 is a time chart for illustrating one scanning period accordingto the second embodiment.

FIG. 14 is a flowchart for illustrating filtering according to thesecond embodiment.

FIG. 15 is a flowchart for illustrating calculation processing of apositional deviation amount according to the second embodiment.

FIG. 16A is a diagram for illustrating uneven image density in theconventional art.

FIG. 16B is a diagram for illustrating positional deviation of scanninglines.

FIG. 17 is a diagram for showing a conversion table for converting imagedata (density data) into drive data for generating a PWM signal.

DESCRIPTION OF THE EMBODIMENTS

Exemplary embodiments of the present invention will be described indetail below in an illustrative manner with reference to the drawings. Adirection of an axis of rotation of a photosensitive drum, which is adirection in which scanning is performed with a laser beam, is definedas a main scanning direction which is a second direction, and arotational direction of the photosensitive drum, which is a directionsubstantially orthogonal to the main scanning direction, is defined as asub-scanning direction witch is a first direction.

First Embodiment Overall Configuration of Image Forming Apparatus

FIG. 1A is a schematic cross-sectional view of a digital full-colorprinter (color image forming apparatus) configured to perform imageformation by using toners of a plurality of colors. An image formingapparatus 100 according to a first embodiment will be described withreference to FIG. 1A. The image forming apparatus 100 includes fourimage forming portions (image forming units) 101Y, 101M, 101C, and 101Bk(broken line portions) respectively configured to form images ofdifferent colors. The image forming portions 101Y, 101M, 101C, and 101Bkform images by using toners of yellow, magenta, cyan, and black,respectively. Reference symbols Y, M, C, and Bk denote yellow, magenta,cyan, and black, respectively, and suffixes Y, M, C, and Bk are omittedin the description below unless a particular color is described.

The image forming portions 101 each include a photosensitive drum 102,being a photosensitive member. A charging device 103, a light scanningdevice 104, and a developing device 105 are arranged around each of thephotosensitive drums 102. A cleaning device 106 is further arrangedaround each of the photosensitive drums 102. An intermediate transferbelt 107 of an endless belt type is arranged under the photosensitivedrums 102. The intermediate transfer belt 107 is stretched around adrive roller 108 and driven rollers 109 and 110, and rotates in adirection of an arrow B (clockwise direction) illustrated in FIG. 1Awhile forming an image. Further, primary transfer devices 111 arearranged at positions opposed to the photosensitive drums 102 across theintermediate transfer belt 107 (intermediate transfer member). The imageforming apparatus 100 according to the embodiment further includes asecondary transfer device 112 configured to transfer the toner image onthe intermediate transfer belt 107 onto a sheet S being a recordingmedium and a fixing device 113 configured to fix the toner image on thesheet S.

An image forming process from a charging step to a developing step ofthe image forming apparatus 100 will be described. The image formingprocess is the same in each of the image forming portions 101, and hencethe image forming process will be described with reference to an exampleof the image forming portion 101Y. Accordingly, descriptions of theimage forming processes in the image forming portions 101M, 101C, and101Bk are omitted. The photosensitive drum 102Y which is driven torotate in the arrow direction (counterclockwise direction) illustratedin FIG. 1A is charged by the charging device 103Y of the image formingportion 101Y. The charged photosensitive drum 102Y is exposed by a laserbeam emitted from the light scanning device 104Y, which is indicated bythe dashed dotted line. With this operation, an electrostatic latentimage is formed on the rotating photosensitive drum 102Y (on thephotosensitive member). The electrostatic latent image formed on thephotosensitive drum 102Y is developed as a toner image of yellow by thedeveloping device 105Y. The same step is performed also in the imageforming portions 101M, 101C, and 101Bk.

The image forming process from a transfer step will be described. Theprimary transfer devices 111 applied with a transfer voltage transfertoner images of yellow, magenta, cyan, and black formed on thephotosensitive drums 102 of the image forming portions 101 onto theintermediate transfer belt 107. With this, the toner images ofrespective colors are superimposed one on another on the intermediatetransfer belt 107. That is, the toner images of four colors aretransferred onto the intermediate transfer belt 107 (primary transfer).The toner images of four colors transferred onto the intermediatetransfer belt 107 are transferred onto the sheet S conveyed from amanual feed cassette 114 or a sheet feed cassette 115 to a secondarytransfer portion by the secondary transfer device 112 (secondarytransfer). Then, the unfixed toner images on the sheet S are heated andfixed onto the sheet S by the fixing device 113, to thereby form afull-color image on the sheet S. The sheet S having the image formedthereon is delivered to a delivery portion 116.

<Photosensitive Drum and Light Scanning Device>

FIG. 1B is an illustration of configurations of the photosensitive drum102, the light scanning device 104, and a controller for the lightscanning device 104. The light scanning device 104 includes a laserlight source 201, a collimator lens 202, a cylindrical lens 203, and arotary polygon mirror 204. The laser light source 201 includes aplurality of light emitting points. The plurality of light emittingpoints are each configured to emit a laser beam (light beam). Thecollimator lens 202 is configured to collimate the laser beam. Thecylindrical lens 203 condenses the laser beam having passed through thecollimator lens 202 in a sub-scanning direction. In the embodiment, thelaser light source 201 is described by exemplifying a light source inwhich a plurality of light emitting points are arranged, but issimilarly operated also in the case of using a single light source. Thelaser light source 201 is driven by a laser drive circuit 304. Therotary polygon mirror 204 is formed of a motor portion configured to beoperated to rotate and a reflection mirror mounted on a motor shaft. Aface of the reflection mirror of the rotary polygon mirror 204 ishereinafter referred to as “mirror face”. The rotary polygon mirror 204is driven by a rotary polygon mirror drive portion 305. The lightscanning device 104 includes fθ lenses 205 and 206 configured to receivea laser beam (scanning light) deflected by the rotary polygon mirror204. Further, the light scanning device 104 includes a memory (storageunit) 302 configured to store various pieces of information.

Further, the light scanning device 104 includes a beam detector 207(hereinafter referred to as “BD 207”) which is a signal generating unitconfigured to detect the laser beam deflected by the rotary polygonmirror 204 and output a horizontal synchronization signal (hereinafterreferred to as “BD signal”) in accordance with the detection of thelaser beam. The laser beam output from the light scanning device 104scans the photosensitive drum 102. The scanning direction of the laserbeam is substantially parallel to the rotary shaft of the photosensitivedrum 102. Every time the mirror face of the rotary polygon mirror 204scans the photosensitive drum 102, the light scanning device 104 causesa laser beam emitted from the laser light source to scan thephotosensitive drum 102 in the main scanning direction, to thereby formscanning lines corresponding to the number of laser elementssimultaneously. In the embodiment, a configuration is described in whichthe rotary polygon mirror 204 has five mirror faces, and the laser lightsource 201 includes eight laser elements, as an example. That is, in theembodiment, an image of eight lines is formed with one scanning, and therotary polygon mirror 204 scans the photosensitive drum 102 five timesper one revolution of the rotary polygon mirror 204, to thereby form animage of forty lines in total.

The photosensitive drum 102 includes a rotary encoder 301 on the rotaryshaft, and the rotation speed of the photosensitive drum 102 is detectedwith use of the rotary encoder 301. The rotary encoder 301 serving as adetection unit generates 1,000 pulses per one revolution of thephotosensitive drum 102, and outputs information on the rotation speed(rotation speed data) of the photosensitive drum 102 based on theresults obtained by measuring a time interval between the pulsesgenerated with use of a built-in timer to a CPU 303. A known speeddetection technology other than the above-mentioned rotary encoder 301may be used as long as the rotation speed of the photosensitive drum 102can be detected. As a method other than the use of the rotary encoder301, there is given, for example, a configuration to detect the surfacespeed of the photosensitive drum 102 with a laser Doppler.

Next, the CPU 303 serving as the controller for the light scanningdevice 104 and a clock signal generating portion 308 will be describedwith reference to FIG. 2. The CPU 303 and the clock signal generatingportion 308 are mounted on the image forming apparatus 100. FIG. 2 is ablock diagram for illustrating the functions of the CPU 303 configuredto execute correction processing of correcting distortion and unevenimage density of an image described later. The CPU 303 includes afiltering portion 501, an error diffusion processing portion 502, and apulse width modulation (PWM) signal generating portion 503. Thefiltering portion 501 is configured to perform filtering by subjectinginput image data to a convolution operation. The error diffusionprocessing portion 502 is configured to subject the image data after thefiltering to error diffusion processing. The PWM signal generatingportion 503 is configured to subject the image data (density data) afterthe error diffusion processing to PWM transformation and output a PWMsignal to the laser drive circuit 304 of the light scanning device 104.The clock signal generating portion 308 is configured to output a clocksignal CLK(1) and a clock signal CLK(2) to the CPU 303. The clock signalCLK(1) is a clock signal illustrated in FIG. 13 described later. Theclock signal CLK(1) is a signal generated by multiplying the clocksignal CLK(2). Thus, the clock signal CLK(1) and the clock signal CLK(2)have a synchronization relationship. In the embodiment, the clock signalgenerating portion 308 outputs the clock signal CLK(1) generated bymultiplying the clock signal CLK(2) by 16 to the CPU 303. The clocksignal CLK(2) is a signal having a period corresponding to one pixel.The clock signal CLK(1) is a signal having a period corresponding todivided pixels obtained by dividing one pixel by 16.

Further, the CPU 303 includes a filter coefficient setting portion 504,a filter function output portion 505, and a correction value settingportion 506. The filter function output portion 505 is configured tooutput data on a function to be used for a convolution operation (forexample, data in a table) to the filter coefficient setting portion 504.As a function to be used for the convolution operation, there is given,for example, linear interpolation and bicubic interpolation. Thecorrection value setting portion 506 is configured to identify a mirrorface which reflects a laser beam from among a plurality of mirror facesbased on a face synchronization signal input from a face identifyingportion 507. The correction value setting portion 506 is configured todetermine a positional deviation amount in the rotation direction of thephotosensitive drum 102 of a scanning line formed with a laser beamdeflected by the mirror face identified by the face identifying portion507 described later. The correction value setting portion 506 thencalculates a correction value based on the positional deviation amountof the scanning line and output the calculated correction value to thefilter coefficient setting portion 504. The filter coefficient settingportion 504 is configured to calculate a filter coefficient to be usedfor the filtering in the filtering portion 501 based on information onthe convolution function input from the filter function output portion505 and the correction value input from the correction value settingportion 506. The filter coefficient setting portion 504 is configured toset the calculated filter coefficient in the filtering portion 501. Thecorrection value input to the filter coefficient setting portion 504from the correction value setting portion 506 is a correction value setindividually for each of the plurality of mirror faces.

Further, the CPU 303 includes the face identifying portion 507. The faceidentifying portion 507 is configured to identify a mirror face of therotary polygon mirror 204 based on an HP signal input from a homeposition sensor (hereinafter referred to as “HP sensor”) 307 of thelight scanning device 104 and the BD signal input from the BD 207. Theface identifying portion 507 is configured to output information of theidentified mirror face to the correction value setting portion 506 as aface synchronization signal.

The CPU 303 is configured to receive image data from an image controller(not shown) configured to generate image data. The image data isgradation data indicating a density value. The gradation data is data ofa plurality of bits indicating a density value for each pixel. Forexample, in the case of image data of 4 bits, a density value of onepixel is expressed by 16 gradations, and in the case of image data of 8bits, a density value of one pixel is expressed by 256 gradations. Inthe embodiment, the image data input to the CPU 303 from the imagecontroller is 4 bits per pixel. The filtering portion 501 is configuredto subject the image data to filtering for each pixel in synchronizationwith the clock signal CLK(2). The CPU 303 is connected to the rotaryencoder 301, the BD 207, the memory 302, the laser drive circuit 304,and the rotary polygon mirror drive portion (hereinafter referred to as“mirror drive portion”) 305. The CPU 303 is configured to detect a writeposition of a scanning line based on the BD signal input from the BD 207and count a time interval of the BD signal, to thereby detect therotation speed of the rotary polygon mirror 204. Further, the CPU 303 isconfigured to output an acceleration or deceleration signal fordesignating acceleration or deceleration to the mirror drive portion 305so that the rotary polygon mirror 204 reaches a predetermined speed. Themirror drive portion 305 is configured to supply a driving current tothe motor portion of the rotary polygon mirror 204 in accordance withthe acceleration or deceleration signal input from the CPU 303, tothereby drive a motor 306.

The HP sensor 307 is mounted on the rotary polygon mirror 204 and isconfigured to output the HP signal to the CPU 303 at timing at which therotary polygon mirror 204 reaches a predetermined angle during arotation operation. For example, the HP signal is generated once duringevery rotation of the rotary polygon mirror 204. The face identifyingportion 507 resets an internal counter in response to the generation ofthe HP signal. Then, the face identifying portion 507 increments a countvalue of the internal counter by “1” every time the BD signal is input.That is, the count values of the internal counter are informationindicating the plurality of mirror faces of the rotary polygon mirror204, respectively. The CPU 303 can identify which of the plurality ofmirror faces the input image data corresponds to with use of the countvalue. That is, the CPU 303 can switch a filter coefficient forcorrecting the input image data with use of the count value.

The memory 302 is configured to store, for each mirror face, positioninformation (first scanning position information) indicating positionaldeviation amounts from ideal scanning positions in the sub-scanningdirection of a plurality of laser beams reflected by the mirror faces ofthe rotary polygon mirror 204. Further, the memory 302 is configured tostore position information (second scanning position information)indicating a positional deviation amount from the ideal scanningposition in the sub-scanning direction of the laser beam emitted fromeach light emitting point. The CPU 303 is configured to read each of thefirst scanning position information and the second scanning positioninformation. The CPU 303 is configured to calculate the position of eachscanning line based on the position information read from the memory 302and calculate image data taking information for correcting the positionof each scanning line into account from the calculated position of eachscanning line and the input image data. The PWM signal generatingportion 503 of the CPU 303 is configured to convert the image datataking the information for correcting the position of each scanning lineinto account into drive data. A ROM 309 is configured to store aconversion table for converting image data of 4 bits into drive data of16 bits as shown in FIG. 17. A vertical axis of the conversion tableshown in FIG. 17 represents image data indicating density values of 4bits, which corresponds to one pixel. A horizontal axis of theconversion table shown in FIG. 17 represents drive data of bitsassociated with the density values of 4 bits individually. For example,in the case where image data input to the PWM signal generating portion503 is a bit pattern of “0110”, the PWM signal generating portion 503converts the image data “0110” into drive data that is a bit pattern of“0000000000111111” with use of the conversion table. The PWM signalgenerating portion 503 outputs the converted drive data in the order of“0000000000111111” serially on a bit basis in accordance with the clocksignal (1) described later. When the PWM signal generating portion 503outputs the drive data, a PWM signal is generated. When the PWM signalgenerating portion 503 outputs “1”, a light emitting point emits a laserbeam. When the PWM signal generating portion 503 outputs “0”, a lightemitting point does not output a laser beam.

<Scanning Position Information>

Next, scanning position information stored in the memory 302 will bedescribed with reference to FIG. 3 and Table 1.

FIG. 3 is an illustration of a state of positional deviation of eachscanning line from an ideal position. Scanning lines scanned by eachlaser beam of the laser light source having eight light emitting pointsare denoted by LD1, LD2, LD3, LD4, LD5, LD6, LD7, and LD8. An idealinterval between the respective scanning lines is determined based on aresolution. For example, in the case of an image forming apparatushaving a resolution of 1,200 dpi, an ideal interval between therespective scanning lines is 21.16 μm. When the scanning line LD1 isdefined as a reference position, ideal distances D2 to D8 of thescanning lines LD2 to LD8 from the scanning line LD1 are calculated byExpression (1).

Dn=(n−1)×21.16 μm (n=2 to 8)  Expression (1)

For example, the ideal distance D4 from the scanning line LD1 to thescanning line LD4 is 63.48 μm (=(4−1)×21.16 μm).

In this case, an interval between the scanning lines on thephotosensitive drum 102 has an error due to an error of arrangementintervals of the plurality of light emitting points and characteristicsof a lens. The positional deviation amounts of the scanning linepositions of the scanning lines LD2 to LD8 with respect to idealpositions determined based on the ideal distances D2 to D8 are denotedby X1 to X7. Regarding the first face of the rotary polygon mirror 204,for example, the positional deviation amount X1 of the scanning line LD2is defined as a difference between the ideal position of the scanningline LD2 (hereinafter referred to as “LINE 2”, which similarly appliesto the other scanning lines) and the actual scanning line. Further, forexample, the positional deviation amount X3 of the scanning line LD4 isdefined as a difference between the LINE 4 and the actual scanning line.

Due to a variation in manufacturing of each mirror face of the rotarypolygon mirror 204, the mirror faces of the rotary polygon mirror 204are not completely parallel to the rotary shaft, and the rotary polygonmirror 204 has an angle variation for each mirror face. The positionaldeviation amounts with respect to the ideal positions in each mirrorface of the rotary polygon mirror 204 are denoted by Y1 to Y5 when thenumber of the mirror faces of the rotary polygon mirror 204 is five. InFIG. 3, a deviation amount of the scanning line LD1 from the idealposition (LINE 1) in the first face of the rotary polygon mirror 204 isdenoted by Y1, and a deviation amount of the scanning line LD1 in thesecond face of the rotary polygon mirror 204 from the ideal position(LINE 9) is denoted by Y2.

A mirror face of the rotary polygon mirror 204 is defined as an m-thface, and a positional deviation amount of a scanning line (LDn) by ann-th laser beam from the laser light source is denoted by Zmn. Then, thepositional deviation amount Zmn is represented by Expression (2) withuse of the positional deviation amounts X1 to X7 of each scanning lineand the positional deviation amounts Y1 to Y5 of each mirror face.

Zmn=Ym+X(n−1)(m=1 to 5,n=1 to 8)  Expression (2)

(Where X(0)=0.)

For example, a positional deviation amount Z14 regarding the scanningline LD4 in the first face of the rotary polygon mirror 204 isdetermined to be Z14=Y1+X3 by Expression (2). Further, a positionaldeviation amount Z21 regarding the scanning line LD1 in the second faceof the rotary polygon mirror 204 is determined to be Z21=Y2 byExpression (2).

When the positional deviation amount Zmn is calculated by Expression(2), it is only necessary that the number of pieces of data to be usedfor calculating the positional deviation amount Zmn correspond to thenumber of the mirror faces of the rotary polygon mirror 204 and thenumber of light emitting points of the laser light source. An addressmap of positional deviation data stored in the memory 302 is shown inTable 1.

TABLE 1 Address Data 0 LD2 Position Information X1 1 LD3 PositionInformation X2 2 LD4 Position Information X3 3 LD5 Position InformationX4 4 LD6 Position Information X5 5 LD7 Position Information X6 6 LD8Position Information X7 7 First Face Position Information Y1 8 SecondFace Position Information Y2 9 Third Face Position Information Y3 10Fourth Face Position Information Y4 11 Fifth Face Position InformationY5

As shown in Table 1, information on the respective positional deviationamounts (described as position information) X1 to X7 of the scanningline LD2 to the scanning line LD8 is stored in from an address 0 to anaddress 6 of the memory 302. Further, information on the respectivepositional deviation amounts Y1 to Y5 of the first face to the fifthface of the mirror faces of the rotary polygon mirror 204 is stored infrom an address 7 to an address 11 of the memory 302. In the embodiment,description is given on the assumption that the eight scanning lines ofeach laser beam are deviated uniformly due to the positional deviationof each mirror face of the rotary polygon mirror 204. That is, in theembodiment, twelve pieces of position information are stored in thememory 302. However, when there is a variation in positional deviationamount of each scanning line of a laser beam for each mirror face of therotary polygon mirror 204, there may be stored information on apositional deviation amount only for a combination of each mirror faceof the rotary polygon mirror 204 and each scanning line of the laserbeam. That is, in this case, forty pieces of position information arestored in the memory 302 with the number of the mirror faces of therotary polygon mirror 204 being five, and the number of light emittingpoints of the laser light source being eight.

(Memory Storage Operation)

As information on a positional deviation amount to be stored in thememory 302, for example, data measured in an adjustment step of thelight scanning device 104 in a factory or the like is stored. Further,the image forming apparatus 100 may include a position detection unitconfigured to detect the position of a scanning line scanned with alaser beam emitted from the laser light source 201 so that theinformation stored in the memory 302 may be updated in real time. As theposition detection unit configured to detect a position of scanninglight in the sub-scanning direction, a known technology may be used. Forexample, a position may be detected by a CMOS sensor or a positionsensitive detector (PSD) arranged in the light scanning device 104 orarranged on a scanning path of a laser beam near the photosensitive drum102. Further, a triangular slit may be formed in a surface of a photodiode (PD) arranged in the light scanning device 104 or arranged nearthe photosensitive drum 102, to thereby detect a position from an outputpulse width of the PD.

FIG. 4 is a block diagram for illustrating a step of storing informationin the memory 302 of the light scanning device 104 in a factory or thelike as an example. The same configurations as those of FIG. 2 aredenoted by the same reference symbols as those therein, and thedescription thereof is omitted. In the adjustment step for the lightscanning device 104, a measuring instrument 400 is arranged at aposition corresponding to the scanning position on the photosensitivedrum 102 when the light scanning device 104 is mounted on the imageforming apparatus 100. The measuring instrument 400 includes a measuringportion 410 and a calculation portion 402, and the calculation portion402 is configured to receive a face synchronization signal from the faceidentifying portion 507 of the CPU 303 of FIG. 2. In the CPU 303 of FIG.4, only the face identifying portion 507 is illustrated. First, a laserbeam is radiated to the measuring portion 410 from the light scanningdevice 104. The measuring portion 410 includes a triangular slit 411 anda PD 412. A laser beam emitted from the light scanning device 104indicated by the arrow with the alternate long and short dash line inFIG. 4 scans the triangular slit 411. The measuring portion 410 measuresthe position in the sub-scanning direction of a scanning line based oninformation on the laser beam input to the PD 412 through the triangularslit 411. The measuring portion 410 outputs information on the measuredposition in the sub-scanning direction of the scanning line in eachmirror face (hereinafter referred to as “data for each face”) of therotary polygon mirror 204 to the calculation portion 402.

Meanwhile, the face identifying portion 507 is configured to receive theHP signal from the HP sensor 307 of the light scanning device 104 andreceive the BD signal from the BD 207. With this, the face identifyingportion 507 is configured to identify a mirror face of the rotarypolygon mirror 204 and output information on the identified mirror faceto the calculation portion 402 as a face synchronization signal. Thecalculation portion 402 is configured to write the information on theposition in the sub-scanning direction of the scanning line measured bythe measuring portion 410 into an address on the memory 302 of the lightscanning device 104 in accordance with the information on the mirrorface of the rotary polygon mirror 204 input from the face identifyingportion 507. Thus, the information on the positional deviation amountsof the scanning lines caused by a variation in intervals between theeight light emitting points of the laser light source 201 (X1 to X7) andthe information on the positional deviation amounts of the scanninglines caused by an optical face tangle error of the mirror face of therotary polygon mirror 204 (Y1 to Y5) are stored in the memory 302.

(Correction of Position in Sub-Scanning Direction of Pixel of InputImage)

In the embodiment, the CPU 303 is configured to correct image data basedon the positional deviation amounts in the sub-scanning direction of thescanning lines formed by laser beams and output drive data generatedbased on the corrected image data to the laser drive circuit 304. Now, aflowchart of FIG. 5 will be described below. FIG. 5 is a flowchart forillustrating correction processing for correcting uneven image densityand banding caused by the positional deviation in the sub-scanningdirection. In Step S3602, the CPU 303 reads the positional deviationamount in the sub-scanning direction stored in the memory 302.Specifically, the CPU 303 reads the position information X1 to X7 of thescanning lines LD2 to LD 8 and the position information Y1 to Y5 of thefirst to fifth faces of the rotary polygon mirror 204 shown in Table 1from the memory 302. In the embodiment, the pixel position in thesub-scanning direction of the input image data is corrected based on thepositional deviation amount in the sub-scanning direction, followed bythe filtering, to thereby output pixel data.

(State of Positional Deviation of Scanning Line)

The state of positional deviation of a scanning line can be roughlyclassified into four cases. First, regarding the state of positionaldeviation, there is a case (a) in which the position of a scanning line(hereinafter referred to as “scanning position”) on the photosensitivedrum 102 is shifted in an advance direction with respect to an idealscanning position, and a case (b) in which the scanning position on thephotosensitive drum 102 is shifted in a return direction with respect tothe ideal scanning position. Further, regarding the state of positionaldeviation, there is a case (c) in which the scanning positions on thephotosensitive drum 102 are dense with respect to the ideal scanningpositions, and a case (d) in which the scanning positions on thephotosensitive drum 102 are sparse with respect to the ideal scanningpositions. Specific examples of the state of positional deviation in thesub-scanning direction are illustrated in FIG. 6A, FIG. 6B, FIG. 6C, andFIG. 6D. In FIG. 6A to FIG. 6D, the broken lines represent scanningpositions, and in FIG. 6A to FIG. 6D, (1) to (5) represent the order ofscanning. In the embodiment, eight beams are used for scanningsimultaneously, but description is given on the assumption that theorder is allocated to each beam arranged successively in thesub-scanning direction. Each column on the left side of FIG. 6A to FIG.6D represents ideal scanning positions, and each column on the rightside represents scanning positions on the photosensitive drum 102. S1 toS5 represent positional deviation amounts from the ideal scanningpositions with respect to scanning numbers (1) to (5). The unit of apositional deviation amount is represented based on the case where theideal beam interval (21.16 μm at 1,200 dpi) is defined as 1, and theadvance direction of a laser beam in the sub-scanning direction(hereinafter simply referred to as “advance direction”) is set to apositive value. Further, the return direction of the laser beam in thesub-scanning direction (hereinafter simply referred to as “returndirection”) is set to a negative value. Further, in order to describethe state of an image, each pixel arranged in the sub-scanning directionis represented by a circle on the scanning line. The shading of thecircle represents density.

FIG. 6A is an illustration of an example in which the scanning positionson the photosensitive drum 102 are shifted by 0.2 uniformly in theadvance direction from the ideal scanning positions. The positionaldeviation amount as illustrated in FIG. 6A is hereinafter referred to asa shift amount of +0.2. FIG. 6B is an illustration of an example inwhich the scanning positions on the photosensitive drum 102 are shiftedby 0.2 uniformly in the return direction from the ideal scanningpositions. The positional deviation amount as illustrated in FIG. 6B ishereinafter referred to as a shift amount of −0.2. In FIG. 6A and FIG.6B, the scanning positions are shifted uniformly, and hence the intervalbetween the scanning positions on the photosensitive drum 102 is 1 inboth the cases.

In FIG. 6C, the positional deviation amount is 0 at a predeterminedscanning position on the photosensitive drum 102. However, as thescanning position returns backward from the scanning position of thepositional deviation amount of 0, the positional deviation amount in theadvance direction increases, and as the scanning position proceedsforward from the scanning position of the positional deviation amount of0, the positional deviation amount in the return direction increases.For example, S3 is +0 in the scanning number (3), but S2 is +0.2 in thescanning number (2), S1 is +0.4 in the scanning number (1), S4 is −0.2in the scanning number (4), and S5 is −0.4 in the scanning number (5).In FIG. 6C, the interval between the scanning positions is 0.8, which issmaller than 1. The state of positional deviation as illustrated in FIG.6C is hereinafter referred to as being dense at an interval of a (1−0.2)line.

In FIG. 6D, the positional deviation amount is 0 at a predeterminedscanning position on the photosensitive drum 102. However, as thescanning position returns backward from the scanning position of thepositional deviation amount of 0, the positional deviation amount in thereturn direction increases, and as the scanning position proceedsforward from the scanning position of the positional deviation amount of0, the positional deviation amount in the advance direction increases.For example, S3 is +0 in the scanning number (3), but S2 is −0.2 in thescanning number (2), S1 is −0.4 in the scanning number (1), S4 is +0.2in the scanning number (4), and S5 is +0.4 in the scanning number (5).In FIG. 6D, the interval between the scanning positions is 1.2, which islarger than 1. The state of positional deviation as illustrated in FIG.6D is hereinafter referred to as being sparse at an interval of a(1+0.2) line.

In the dense state as illustrated in FIG. 6C, positional deviationoccurs, and in addition, the scanning positions are dense to causepixels to be arranged densely on the photosensitive drum 102, with theresult that a pixel value per predetermined area increases, to therebyincrease density. In contrast, in the sparse state as illustrated inFIG. 6D, positional deviation occurs, and in addition, the scanningpositions are sparse to cause pixels to be arranged sparsely on thephotosensitive drum 102, with the result that a pixel value perpredetermined area decreases, to thereby decrease density. In anelectrophotographic process, a shading difference may be furtheremphasized due to a relationship between the depth of a latent imagepotential and development characteristics. Further, when the dense orsparse state occurs alternately as illustrated in FIG. 6C and FIG. 6D, aperiodic shading causes moire, which is liable to be detected visuallyeven at the same amount depending on a space frequency.

Referring back to the flowchart of FIG. 5, in Step S3603, the CPU 303generates attribute information for correction of each pixel of an inputimage with the correction value setting portion 506. In the embodiment,the pixel position in the sub-scanning direction of an input image issubjected to coordinate transformation in advance and interpolated,thereby being capable of correcting positional deviation and correctinglocal shading simultaneously while maintaining density of the inputimage. The attribute information for correction specifically refers to acorrection value C described later.

(Coordinate Transformation)

A method for coordinate transformation according to the embodiment willbe described with reference to FIG. 7A, FIG. 7B, FIG. 8A, FIG. 8B, FIG.8C, FIG. 8D, FIG. 9A, and FIG. 9B. In each graph of FIG. 7A to FIG. 9B,a horizontal axis represents a pixel number n, and a vertical axisrepresents a pixel position (which is also a scanning position) y (y′after the coordinate transformation) in the sub-scanning direction, withthe unit being a line. Further, FIG. 7A, FIG. 7B, FIG. 9A, and FIG. 9Bcorrespond to FIG. 6A, FIG. 6B, FIG. 6C, and FIG. 6D, respectively. Eachgraph on the left side of FIG. 7A, FIG. 7B, FIG. 9A, and FIG. 9Brepresents the state before the coordinate transformation, and eachgraph on the right side thereof represents the state after thecoordinate transformation for the y-axis. Square dots plotted in eachgraph represent scanning positions on the photosensitive drum 102, andcircular dots therein represent ideal scanning positions.

(Case of being Shifted in Advance Direction and Return Direction)

The graph on the left side of FIG. 7A is first described. In the graphbefore the coordinate transformation, at the ideal scanning positionsplotted with the circular dots, for example, a pixel position “y” in thesub-scanning direction is 2 with respect to the pixel number 2. Thus,the y-coordinate of the pixel position “y” is equal to that of the pixelnumber “n”, and the ideal scanning positions are represented by astraight line (indicated by the alternate long and short dash line) witha gradient of 1. The straight line of the alternate long and short dashline is represented by Expression (3).

y=n  Expression (3)

As illustrated in FIG. 6A, the scanning positions plotted with thesquare dots are shifted by S(=0.2) line in the advance direction (+direction of y-axis) with respect to the ideal scanning positionsplotted with the circular dots. Therefore, the scanning positionsplotted with the square dots are represented by a straight line(indicated by the solid line) offset with the gradient being 1, which isrepresented by Expression (4).

y=n+S  Expression (4)

In the embodiment, the coordinate transformation is performed so thatthe actual scanning positions are transformed into the ideal scanningpositions. Therefore, in the example illustrated in FIG. 7A, it is onlynecessary that the coordinate transformation be performed with use ofExpression (5). In Expression (5), C represents a correction amount.

y′=y+C  Expression (5)

Thus, the correction amount C is represented by a shift amount S andExpression (6).

C=−S  Expression (6)

Through Expression (5) of the coordinate transformation and Expression(6) for determining the correction amount C, Expressions (3) and (4) areconverted as represented by Expressions (7) and (8), respectively.

y′=y+C=n+(−S)=n−S  Expression (7)

y′=y+C=(n+S)+C=(n+S)+(−S)=n  Expression (8)

In FIG. 7B, when the shift amount S is defined as −0.2, Expression (8)similarly holds from Expression (3), and the similar description to thatof FIG. 7A can be given. As illustrated in FIG. 7A and FIG. 7B, when thescanning lines are not sparse or dense, and are shifted in the advancedirection or the return direction, a straight line has a predeterminedgradient before and after the coordinate transformation.

(Case in which Dense and Sparse State Occur)

Now, the coordinate transformation will be described, which is alsoapplicable to the cases in FIG. 9A and FIG. 9B in which the scanningpositions become dense and sparse, and the cases of combinations of FIG.7A, FIG. 7B, FIG. 9A, and FIG. 9B in which a shift and a dense andsparse state occur. FIG. 8A is an illustration of a relationship betweenthe pixel number and the scanning position, and a horizontal axisrepresents a pixel number “n”, and a vertical axis “y” represents ascanning position in the sub-scanning direction, square dots beingplotted as the scanning positions on the photosensitive drum 102. InFIG. 8A, the case is described in which the scanning lines are dense onthe photosensitive drum 102 within a range of the pixel number of n≦2,and the scanning lines are sparse on the photosensitive drum 102 withina range of the pixel number of n≧2.

As illustrated in FIG. 8A, when the scanning lines are dense within therange of the pixel number of n≦2, and are sparse within the range of thepixel number of n≧2, the gradient of a straight line within the range ofthe pixel number of n≦2 is different from that of a straight line withinthe range of the pixel number of n≧2, and the straight line has a curvedshape at the pixel number of n=2. In FIG. 8A, a function indicating achange in scanning positions passing through the square dots is definedas ft(n) and is represented by the solid line. The function ft(n)representing the scanning positions is represented by Expression (9).

y=ft(n)  Expression (9)

Next, when a function after the coordinate transformation of the y-axisthat represents the scanning positions in the sub-scanning direction isdefined as ft′(n), the function ft′(n) representing the scanningpositions after the coordinate transformation is represented byExpression (10).

y′=ft′(n)  Expression (10)

In the embodiment, the coordinate transformation is performed byexpanding or contracting the y-axis or shifting the y-axis so that thescanning positions after the coordinate transformation become uniform.Therefore, the function ft′(n) representing the scanning positions afterthe coordinate transformation satisfies the condition represented byExpression (11).

ft′(n)=n  Expression (11)

Expression (11) means that, for example, a pixel position y′ (=ft′(2))in the sub-scanning direction after the coordinate transformationbecomes 2 with respect to the pixel number 2.

The broken lines connecting FIG. 8A and FIG. 8B to each other representthe correspondence from an original coordinate position of the y-axis toa coordinate position of the y′-axis after the coordinate transformationfrom the left to the right, and indicate a state in which a lower half(corresponding to n≦2) of the y-axis expands, and an upper half(corresponding to n≧2) contracts before and after the coordinatetransformation. A procedure for determining a coordinate after thecoordinate transformation of each pixel of input image data through thecoordinate transformation of FIG. 8A and FIG. 8B will be described withreference to FIG. 8C and FIG. 8D. In the same manner as in FIG. 8A andFIG. 8B, a horizontal axis in FIG. 8C and FIG. 8D represents a pixelnumber “n”, and a vertical axis “y” (or y′) represents scanningpositions in the sub-scanning direction. FIG. 8C is an illustrationbefore the coordinate transformation, and FIG. 8D is an illustrationafter the coordinate transformation. A relationship between the pixelnumber n and the coordinate position y of the input image data will bedescribed below. First, the broken line of FIG. 8C represents a functionfs(n) representing ideal scanning positions before the coordinatetransformation and is represented by Expression (12).

y=fs(n)  Expression (12)

Further, in the embodiment, the interval between the pixels in thesub-scanning direction of the input image data is uniform, and hence thefunction fs(n) is represented by Expression (13).

fs(n)=n  Expression (13)

A scanning position of the y′-coordinate after the coordinatetransformation of a pixel number of interest “ns” of the input imagedata is determined through three steps described below. In the firststep, when the y-coordinate of an ideal scanning position correspondingto the pixel number “ns” of the input image data is defined as “ys”,“ys” can be determined by Expression (14).

ys=fs(ns)  Expression (14)

A pixel number “nt” in which the scanning position before the coordinatetransformation is the same on the photosensitive drum 102 (solid line)is determined ((1) of FIG. 8C). The scanning position on thephotosensitive drum 102 is represented by the function y=ft(n), and arelationship of ys=ft(nt) holds. When an inverse function of thefunction ft(n) is defined as ft⁻¹(y), the pixel number “nt” isrepresented by Expression (15).

nt=ft ⁻¹(ys)  Expression (15)

In the second step, the y′-coordinate after the coordinatetransformation (defined as “yt”) corresponding to the pixel number “nt”of the scanning position on the photosensitive drum 102 is determined byExpression (16) with use of the function ft′(n) after the coordinatetransformation ((2) of FIG. 8D).

yt=ft′(nt)  Expression (16)

The pixel number ns holds even when any number is selected, and hence anexpression for determining the position “yt” of the y′-coordinate afterthe coordinate transformation based on the pixel number ns correspondsto the function fs′(n) for determining the y′-coordinate in calculationbased on the pixel number n of the input image data. Thus, a generalexpression represented by Expression (17) is derived from Expressions(14) to (16). A function indicating the ideal scanning positionrepresented by the broken line after the coordinate transformation isrepresented by y′=fs′(n) ((3) of FIG. 8D).

yt=fs′(ns)=ft′(nt)=ft′(ft⁻¹(ys))=ft′(ft⁻¹(fs(ns))) “ns” is generalizedinto “n” to obtain Expression (17).

fs′(n)=ft′(ft ⁻¹(fs(n)))  Expression (17)

Further, Expression (13) and Expression (11) in which the pixel intervalof the input image data and the interval of the scanning positions afterthe coordinate transformation are set to be uniform, with the distanceof 1, are substituted into Expression (17). Then, Expression (17) isrepresented by Expression (18) with use of the inverse function ft⁻¹(n)of the function ft(n) for deriving the scanning position from the pixelnumber n.

fs′(n)=ft ⁻¹(n)  Expression (18)

Expression (4) in which the scanning positions are shifted uniformly inthe advance direction and the return direction as illustrated in FIG. 7Aand FIG. 7B, and Expression (7) for determining a position after thecoordinate transformation of the input image data also have an inversefunction relationship, and it can be confirmed that Expression (18)holds. Further, when applied to the case in which the dense or sparsestate occurs in scanning positions as illustrated in FIG. 9A and FIG.9B, the function “y” representing scanning positions before thecoordinate transformation is represented by Expression (19) when thefunction “y” is a straight line with a gradient “k”, passing through(n0, y0).

fs(n)=y=k×(n−n0)+y0  Expression (19)

In order to determine a pixel position after the coordinatetransformation of the y-axis of the input image data, it is onlynecessary that an inverse function ((1/k)×(y−y0)+n0) be determined byExpressions (17) and (18), and the pixel number “n” be substituted intothe inverse function, and hence Expression (20) is derived.

y′=(1/k)×(n−y0)+n0  Expression (20)

When the scanning lines illustrated in FIG. 9A are dense, and thescanning lines illustrated in FIG. 9B are sparse, the positions of thescanning lines on the photosensitive drum 102 after the coordinatetransformation can be represented by Expression (20) in both the cases.Further, a correction value Cn of the pixel number n is determined byCn=fs′(n)−fs(n).

Specifically in FIG. 9A, n0=y0=3 and k=0.8 are satisfied, and Expression(21) is obtained.

fs′(n)=(1/0.8)×(n−3)+3  Expression (21)

For example, in the pixel number 3, fs′(3)=3.00 is satisfied, and thecorrection value C3 is 0.00 (=3.00−3.00). Further, in the pixel number5, fs′(5)=5.50 is satisfied, and the correction value C5 is +0.50(=+5.50−5.00). The correction values C1 to C5 when the scanningpositions are dense are illustrated in FIG. 11C.

Further, in FIG. 9B, n0=y0=3, and k=1.2 are satisfied, and Expression(22) is obtained.

fs′(n)=(1/1.2)×(n−3)+3  Expression (22)

For example, in the pixel number 3, fs′(3)=3.000 is satisfied, and thecorrection value C3 is 0.000 (=3.000-3.000). Further, in the pixelnumber 5, fs′(5)=4.667 is satisfied, and the correction value C5 is−0.333 (=4.667−5.000). The correction values C1 to C5 when the scanningpositions are sparse are illustrated in FIG. 11D.

Further, even when a dense and sparse state and a shift are mixed in thescanning lines, an ideal scanning position after the coordinatetransformation can be determined with use of Expression (17) or (18).The correction value setting portion 506 is configured to subject anideal scanning position to the coordinate transformation based on apositional deviation amount to determine the correction value Cn, andoutput information on the correction value Cn to the filter coefficientsetting portion 504.

(Filtering)

In the embodiment, the filtering is performed in order to generatecorrection data. In the embodiment, the filtering portion 501 isconfigured to perform the filtering through a convolution operationbased on the following filter function. That is, the filtering portion501 performs the filtering based on a positional relationship betweenthe pixel positions in the sub-scanning direction of pixels obtained bycorrecting scanning positions in the sub-scanning direction of pixels ofthe input image data, and the sub-scanning positions of pixels having aninterval between scanning lines transformed uniformly by the coordinatetransformation. A pixel before the filtering is also referred to as aninput pixel, and a pixel after the filtering is also referred to as anoutput pixel. Further, a pixel before the filtering is a pixel subjectedto the above-mentioned coordinate transformation.

The convolution function according to the embodiment can be selectedfrom linear interpolation illustrated in FIG. 10A, and bicubicinterpolation illustrated in FIG. 10B and FIG. 10C. The filter functionoutput portion 505 outputs information on the convolution function usedin the filtering to the filter coefficient setting portion 504 asinformation of the table, for example. In FIG. 10A to FIG. 10C, avertical axis “y” represents a position in the sub-scanning direction,with a unit being a pixel, and a horizontal axis “k” represents amagnitude of a coefficient. Although the unit of the vertical axis “y”is set to a pixel, a line may be used as a unit because the sub-scanningdirection is illustrated.

An expression of FIG. 10A is represented by Expression (23).

k=y+1(−1≦y≦0)

k=−y+1(0<y≦1)

0(y<−1,y>1)  Expression (23)

Expressions of FIG. 10B and FIG. 10C are represented by the followingtwo expressions.

$\begin{matrix}{{{bicubic}(t)} = \left\{ \begin{matrix}{{\left( {a + 2} \right){t}^{3}} - {\left( {a + 3} \right){t}^{2}} + 1} & \left( {{t} \leq 1} \right) \\{{a{t}^{3}} + {5a{t}^{2}} + {8a{t}} - {4a}} & \left( {1 < {t} \leq 2} \right) \\0 & \left( {2 < {t}} \right)\end{matrix} \right.} & {{Expression}\mspace{14mu} (24)} \\{k = {{{bicubic}\left( \frac{y}{w} \right)}/w}} & {{Expression}\mspace{14mu} (25)}\end{matrix}$

In the embodiment, “a” is set to −1, and “w” is set to 1 in FIG. 10B andset to 1.5 in FIG. 10C, but “a” and “w” may be adjusted in accordancewith the electrophotographic characteristics of each image formingapparatus. The filter coefficient setting portion 504 is configured tooutput a coefficient (“k” described later) to be used in the filteringto the filtering portion 501 based on the information on the filterfunction obtained from the filter function output portion 505 and theinformation on the correction value C output from the correction valuesetting portion 506.

Now, description is given with reference to FIG. 10D. In FIG. 10D, ahorizontal axis represents a coefficient “k” to be used in thefiltering, and a vertical axis represents a position “y” in thesub-scanning direction. When the filtering portion 501 receives thecorrection value Cn from the correction value setting portion 506, thefiltering portion 501 determines a coefficient “kn” corresponding to thecorrection value Cn with use of the filter function input from thefilter function output portion 505. White circles of FIG. 10D representcoefficients before the coordinate transformation. Further, in FIG. 10D,it is illustrated that coefficients k1 and k2 were set with respect to acorrection value C1 and a correction value C2, respectively, ascoefficients “kn” to be used in the filtering (black circles). In theembodiment, the same convolution function is applied irrespective ofwhether the input image data is dense or sparse, and sampling isperformed at an ideal scanning position, to thereby store density perpredetermined area of the input image data.

(Specific Example of Filtering)

A specific example of performing the filtering with use of theconvolution operation with a filter function by linear interpolation ofExpression (23) based on a coordinate position after the coordinatetransformation of the embodiment will be described with reference toFIG. 11A, FIG. 11B, FIG. 11C, and FIG. 11D. The filtering using theconvolution operation is performed by the filtering portion 501. FIG.11A to FIG. 11D correspond to FIG. 6A to FIG. 6D. Each column on theleft side of FIG. 11A to FIG. 11D represents input pixels after theabove-mentioned coordinate transformation. Further, each column on theright side of FIG. 11A to FIG. 11D represents scanning positions on thephotosensitive drum 102 after the above-mentioned coordinatetransformation. That is, the scanning positions in each column on theright side of FIG. 11A and FIG. 11D have been subjected to thecoordinate transformation so as to have a uniform interval and adistance of 1.

More specifically, the scanning positions in the sub-scanning directionof input pixels after the coordinate transformation are represented by astraight line (y′=fs′(n)) indicated by the alternate long and short dashline of the graph after the coordinate transformation illustrated on theright side of FIG. 7A, FIG. 7B, FIG. 9A, and FIG. 9B. The scanningpositions on the photosensitive drum 102 after the coordinatetransformation are represented by a straight line (y′=fs′(n)) indicatedby the solid line of the graph after the coordinate transformationillustrated on the right side of FIG. 7A, FIG. 7B, FIG. 9A, and FIG. 9B.For example, in FIG. 7A, the shift amount is +0.2 (=S), and hencefs′(n)=y−0.2=n−0.2 is satisfied after the coordinate transformation.

Further, in FIG. 11A to FIG. 11D, the magnitude of a pixel value, thatis, a density value is represented by shading of circles. Further,numbers in parentheses indicate numbers of scanning lines, and are thesame as the pixel numbers illustrated in FIG. 6A to FIG. 6D. In eachgraph at the center of FIG. 11A to FIG. 11D, a horizontal axisrepresents density, and a vertical axis represents a position in thesub-scanning direction. The convolution operation involves developingwaveforms W (W1 to W5 with respect to the pixels (1) to (5)) obtained bymultiplying the filter function based on each coordinate position of aninput image (FIG. 10A) by a pixel value, and adding the waveforms W bysuperimposing.

FIG. 11A is described first. The pixels (1) and (5) represented by whitecircles have a density of 0, that is, a pixel value of 0. Therefore, W1and W5 obtained by multiplying a filter function by a pixel value areboth 0. The pixels (2), (3), and (4) represented by black circles havethe same density, and the maximum values of the waveforms W2, W3, and W4are the same. Thus, the pixels (2), (3), and (4) each result in awaveform obtained by developing the filter function based on the pixelposition of the input pixel. The result of the convolution operation isa sum (ΣWn, n=1 to 5) of all the waveforms.

A pixel value of an output pixel is sampled at the scanning position onthe photosensitive drum 102 after the scanning position is subjected tothe coordinate transformation. Therefore, for example, the pixel value(1) corresponding to the scanning position on the photosensitive drum102 intersects with the waveform W2 at a point P0, and hence iscalculated to be density D1. Further, the pixel value (2) intersectswith the waveform W2 at a point P2 and the waveform W3 at a point P1,respectively, and hence is calculated to be density D1+D2. The pixelvalues (3) to (5) are subsequently determined in a similar manner. Thepixel value (5) does not intersect with any waveform, and hence thepixel value thereof is set to 0. Further, the result obtained bycalculating the pixel values (1) to (5) of FIG. 11B to FIG. 11D arerepresented by shading of pixels in each column on the right side.

The positional deviation of the input pixels is illustrated so as tocorrespond to each pixel in the vertical axis of FIG. 11A to FIG. 11D.The positional deviation amount represented by the vertical axis of FIG.11A to FIG. 11D is information on the positional deviation amountdetermined by an inverse function in accordance with the coordinatetransformation of the scanning positions in the sub-scanning directionof the pixels of the input image. For example, in the case of FIG. 11A,as described with reference to FIG. 7A, the correction amount C of thepositional deviation amount S of the scanning lines is −0.2. Further,for example, in the cases of FIG. 11C and FIG. 11D, the correctionamounts C are calculated with use of Expressions (21) and (22),respectively.

FIG. 11A is an illustration of a state in which the scanning positionsof the scanning lines are shifted in the advance direction in thesub-scanning direction, but the median points of the pixel values areshifted in the return direction, and hence the positions of the medianpoints of the pixel values are corrected. FIG. 11B is an illustration ofa state in which the scanning positions of the scanning lines areshifted in the return direction in the sub-scanning direction, but themedian points of the pixel values are shifted in the advance direction,and hence the positions of the median points of the pixel values arecorrected. FIG. 11C is the case in which the scanning positions aredense, and is an illustration of a state in which the distribution ofdensity is widened due to the convolution operation after the coordinatetransformation to cancel the local concentration of density, to therebycorrect a local change in density. Further, FIG. 11D is the case inwhich the scanning positions are sparse, and is an illustration of astate in which the distribution of density is narrowed due to theconvolution operation after the coordinate transformation to cancel thedispersion of density, to thereby correct a local change in density. Inparticular, the pixel value (3) of FIG. 11D is a density of (100+α)%which is higher than 100%.

(Filtering)

Referring back to FIG. 5, in Step S3604 of FIG. 5, the CPU 303 performsthe filtering with the filtering portion 501 based on the attributeinformation for correction generated in Step S3603. Specifically, theCPU 303 performs a convolution operation and re-sampling with respect tothe above-mentioned input image. The processing of Step S3604 performedby the CPU 303 will be described below in detail with reference to aflowchart of FIG. 12. When the CPU 303 starts the filtering through theconvolution operation with the filtering portion 501, the CPU 303performs the processing in Step S3703 and subsequent steps. In StepS3703, when the spread of the convolution function is defined as L, theCPU 303 extracts lines of an input image within a range of before andafter ±L of the sub-scanning position of a line “yn” of an output imageof interest, that is, the range of a width of 2L (range of from (ys−L)to (ys+L)). In this case, L is defined as a minimum value at which thevalue of the convolution function becomes 0 outside of the range of from+L to −L of the convolution function. For example, in linearinterpolation of FIG. 10A, L is equal to 1. In bicubic interpolation ofFIG. 10B, L is equal to 2. In bicubic interpolation of FIG. 10C, L isequal to 3. The ymin and ymax within a range of from ymin to ymax of thecorresponding input image satisfy the following condition with use ofExpression (18).

ft ⁻¹(ymin)=yn−L,ft ⁻¹(ymax)=yn+L  Expression (26)

When Expression (26) is modified, the ymin and ymax are determined byExpression (27).

ymin=ft(yn−L),ymax=ft(yn+L)  Expression (27)

Thus, the lines of the input image to be extracted with respect to theline “yn” of the output image of interest are lines of all the integerswithin a range of from ymin to ymax.

When the line of the output image of interest is denoted by “yn”, andthe line of the input image to be subjected to the convolution operationis denoted by “ym”, a distance “dnm” is represented by Expression (28).

dnm=yn−ft ⁻¹(ym)  Expression (28)

Thus, in Step S3704, the CPU 303 obtains a coefficient “knm” as aconvolution function g(y) with the filter coefficient setting portion504 by Expression (29).

knm=g(dnm)  Expression (29)

In Step S3705, the CPU 303 refers to the built-in timer which has beenstarted when the BD signal has been received, to thereby determinewhether or not a period of time T1 has elapsed. In this case, the periodof time T1 is a period of time from timing at which the BD signal isoutput to timing at which the laser beam reaches the leading edge of theimage area in the main scanning direction of the photosensitive drum102, and the detail thereof will be described in a second embodiment. InStep S3705, when the CPU 303 determines that the period of time T1 hasnot elapsed, the CPU 303 returns to the processing in Step S3705. Whenthe CPU 303 determines that the period of time T1 has elapsed, the CPU303 proceeds to the processing in Step S3706. In Step S3706, the CPU 303initializes the position “x” in the main scanning direction (set theposition “x” to 1). In Step S3707, the CPU 303 obtains pixel data on theposition in the sub-scanning direction in the input image extracted inStep S3703 and the position “x” of interest in the main scanningdirection. The pixel data is defined as input pixel data Pin_(m). InStep S3708, the CPU 303 performs the convolution operation with thefiltering portion 501. More specifically, the filtering portion 501subjects the corresponding coefficient knm determined in Step S3704 andthe input pixel data Pin_(m) obtained in S3707 to a product-sumoperation, to thereby determine a value Pout_(n) of the pixel ofinterest. The input pixel data Pin_(m) is density of the pixel ofinterest before the filtering, and the value Pout_(n) of the pixel ofinterest is output pixel data and is density of the pixel of interestafter the filtering.

$\begin{matrix}{{Pout}_{n}{\sum\limits_{m}^{all}{k_{nm} \cdot {Pin}_{m}}}} & {{Expression}\mspace{14mu} (30)}\end{matrix}$

Expression (30) corresponds to FIG. 11A to FIG. 11D. The darkness(density) of the circles on the left side in FIG. 11A to FIG. 11Dcorresponds to the input pixel data Pin_(m). D1 and D2 in FIG. 11Acorrespond to k_(nm)×Pin_(m). The darkness (density) of the circles onthe right side in FIG. 11A to FIG. 11D corresponds to Pout_(n).

In Step S3709, the CPU 303 adds 1 to the position “x” in the mainscanning direction. In Step S3710, the CPU 303 determines whether or notone line has been completed, that is, whether or not the scanning hasreached the last pixel in one line. When the CPU 303 determines that oneline has not been completed, the CPU 303 returns to the processing inStep S3707. When the CPU 303 determines that one line has beencompleted, the CPU 303 terminates the filtering. Thus, in theembodiment, distortion and uneven image density of an image caused bythe deviation of an irradiation position due to a variation inarrangement intervals of light emitting points of a laser light sourceand the optical face tangle error of the mirror faces of the rotarypolygon mirror 204 are corrected by subjecting a pixel position of aninput image to the coordinate transformation based on a profile ofpositional deviation in the sub-scanning direction of the input image.Then, the filtering and sampling are performed, thereby being capable ofcancelling positional deviation and local biased density such as bandingwhile maintaining the density of each input image, with the result thata satisfactory image can be obtained.

As described above, according to the embodiment, satisfactory imagequality is obtained by correcting distortion and uneven image density ofan image.

Second Embodiment

The basic configuration of the second embodiment is the same as that ofthe first embodiment, and the second embodiment is different from thefirst embodiment in that the processing is performed in accordance witha flowchart for illustrating correction processing of FIG. 14 instead ofthe flowchart for illustrating the correction processing of FIG. 12 inthe first embodiment. In the embodiment, regarding positional deviationin the sub-scanning direction, an uneven speed of the photosensitivedrum 102 is also corrected in addition to the deviation amounts based onthe face information (Y1 to Y5) and the beam information (X1 to X7) inthe first embodiment.

<Calculation Method for Positional Deviation Amount>

FIG. 13 is an illustration of control timing in one scanning period of alaser beam in the embodiment. (1) represents a CLK signal correspondingto a pixel period per divided pixel ( 1/16 pixel) obtained by dividingone pixel by 16, and (2) represents input timing of the BD signal fromthe BD 207 to the CPU 303. (3) and (4) are each an illustration oftiming at which the CPU 303 outputs drive data (DATA1, DATA2, etc.). (4)represents drive data after the filtering.

With the BD signal output from the BD 207 being a reference, during aperiod of time from timing at which the BD signal is input to the CPU303 to timing at which a subsequent BD signal is input to the CPU 303, aperiod of time from timing at which the BD signal is input to the CPU303 to timing at which the processing of the image data input to the CPU303 is started is defined as T1. Further, during the period of time fromtiming at which the BD signal is input to the CPU 303 to timing at whicha subsequent BD signal is input to the CPU 303, a period of time fromtiming at which the BD signal is input to the CPU 303 to timing at whichthe output of the image data input to the CPU 303 is completed isdefined as T2. After the BD signal is input to the CPU 303, the CPU 303stands by until the predetermined period of time T1 elapses. Then, theCPU 303 starts the filtering of the input image data in synchronizationwith the clock signal CLK(2) to generate drive data successively fromthe processed image data and output the drive data on a bit basis, tothereby output the PWM signal to the laser drive circuit 304. Then,after the predetermined period of time T2 elapses from the input of theBD signal, the CPU 303 finishes the processing of the image data in onescanning line. The CPU 303 calculates, for each scanning, a positionaldeviation amount of the scanning line in the scanning period until thepredetermined period of time T1 elapses from the detection of the BDsignal, that is, while the laser beam scans a non-image area. Then, theCPU 303 causes the filter coefficient setting portion 594 to set afilter coefficient based on the calculated positional deviation amount.Then, the CPU 303 causes, for each scanning, the filtering portion 501to correct the image data with use of the filter coefficient set by thefilter coefficient setting portion 504 until the predetermined period oftime T2 elapses from the elapse of the predetermined period of time T1.

The flowchart of FIG. 14 for illustrating correction processingaccording to the embodiment is different from the flowchart of FIG. 12in the first embodiment in that the processing in Steps S3713 and S3714is added, and the same processing as that of FIG. 12 is denoted by thesame step number as therein. Steps S3703 and S3704 are the sameprocessing as that of FIG. 12, and the description thereof is omitted.In the embodiment, before the processing in the main scanning directionis initialized in Step S3706, the CPU 303 determines in Step S3713whether or not the current scanning line is a leading line in theprocessing of eight lines, more specifically, whether or not a remainder(y %8, % means Modulo operation) obtained by dividing the currentscanning line y by 8 is 1. When the CPU 303 determines in Step S3713that the current scanning line is the leading line of the eight lines,the CPU 303 performs processing for each scanning in Step S3714. Whenthe CPU 303 determines in Step S3713 that the current scanning line isnot a leading line of the eight lines, the CPU 303 proceeds to theprocessing in Step S3705.

(Calculation of Positional Deviation Amount Taking Uneven Speed ofPhotosensitive Drum into Account)

The details of processing for each scanning in Step S3714 will bedescribed with reference to FIG. 15. FIG. 15 is a flowchart forillustrating processing of calculating a positional deviation amountperformed by the CPU 303. The CPU 303 is configured to calculate apositional deviation amount for each scanning line at a time of imageformation, to thereby perform the control once per scanning. In StepS7002, the CPU 303 determines whether or not the BD signal has beeninput from the BD 207. When the CPU 303 determines in Step S7002 thatthe BD signal has been input, the CPU 303 stops a timer (not shown)measuring a time interval which is a period of the BD signal, reads atimer value, and stores the timer value in an internal register. Then,in order to measure a time interval up to a time when the next BD signalis received, the CPU 303 resets and starts the timer (not shown) andproceeds to processing in Step S7003. In the case where the CPU 303includes two or more timers (not shown), different timers may be usedalternately every time the BD signal is received, to thereby measure atime interval. Further, in this case, the measured time interval of theBD signal is stored in the internal register of the CPU 303, but themeasured time interval may be stored in, for example, a RAM (not shown)serving as a storage unit for the CPU 303. When the CPU 303 determinesin Step S7002 that the BD signal has not been input, the CPU 303 repeatsthe control in Step S7002 so as to wait for the input of the BD signal.

In Step S7003, the CPU 303 reads rotation speed data of thephotosensitive drum 102 from the rotary encoder 301. In Step S7004, theCPU 303 calculates a printing speed Vpr based on the time interval ofthe BD signal stored in the internal register. The printing speed Vpr iscalculated by dividing a value, which is obtained by multiplying thenumber of beams of the laser light source 201 by the interval of thescanning lines, by ΔT (time interval of the BD signal). For example, inthe case of the embodiment, the number of beams is eight, and theinterval of the scanning lines is 21.16 μm (resolution: 1,200 dpi), andhence Vpr=(8×21.16 μm)/ΔT is satisfied. A rotation speed Vp of therotary polygon mirror 204 has a proportional relationship with theprinting speed Vpr, and hence can be determined from the calculatedprinting speed Vpr. In Step S7005, the CPU 303 calculates a positionaldeviation amount A based on the rotation speed of the photosensitivedrum 102 read in Step S7003 and the rotation speed of the rotary polygonmirror 204 calculated in Step S7004. A calculation method for thepositional deviation amount A will be described in detail later.

In Step S7006, the CPU 303 reads face information (Y1 to Y5 in Table 1)and beam position information (X1 to X7 in Table 1) of the rotarypolygon mirror 204 from the memory 302. In Step S7007, the CPU 303calculates a positional deviation amount B (=Zmn) with use of Expression(2) based on the face information and the beam position information readin Step S7006. In Step S7008, the CPU 303 adds up the positionaldeviation amount A calculated in Step S7005 and the positional deviationamount B calculated in Step S7007, to thereby calculate a sum (totalvalue) of the positional deviation amounts. In Step S7009, the CPU 303stores the sum positional deviation amount calculated in Step S7008 inthe internal register of the CPU 303. In this case, the positionaldeviation amount stored in the internal register is read and used forcalculation at a time of filtering described in detail later.

(Calculation of Positional Deviation Amount)

A calculation expression of the positional deviation amount A calculatedby the CPU 303 in Step S7005 will be described in detail. When therotation speed of the photosensitive drum 102 is denoted by Vd, therotation speed of the rotary polygon mirror 204 is denoted by Vp, andone scanning period is denoted by ΔT (see FIG. 13), the positionaldeviation amount A caused by a speed difference between the rotationspeed Vd of the photosensitive drum 102 and the rotation speed Vp of therotary polygon mirror 204 is calculated by Expression (31).

A=(Vd−Vp)×ΔT  Expression (31)

In Expression (31), ΔT represents a period of time corresponding to aninterval of output timing of the BD signal, and the positional deviationamount A represents a positional deviation amount of scanning lines thatmove during one scanning period due to the difference between therotation speed Vd of the photosensitive drum 102 and the rotation speedVp of the rotary polygon mirror 204. As described above, the rotationspeed Vp of the rotary polygon mirror 204 is determined based on theprinting speed Vpr. Then, the printing speed Vpr is determined based onthe relationship between the one scanning period ΔT and the number oflight emitting points (the light emitting points are eight in theembodiment) by Expressions (32) and (33).

Vp=Number of beams×21.16/ΔT  Expression (32)

ΔT=1/(Number of mirror faces of rotary polygon mirror 204×Revolutionsper second of rotary polygon mirror 204)   Expression (33)

When the positional deviation caused by an uneven speed of thephotosensitive drum 102 of the n-th scanning line from the referenceposition in the sub-scanning direction is denoted by An, the positionaldeviation in the sub-scanning direction is represented by anaccumulation of the positional deviation of each scanning. Further, whenthe positional deviation amount based on the face information of therotary polygon mirror 204 of the n-th scanning line from the referenceposition in the sub-scanning direction and the beam information isdenoted by Bn, the position y in the sub-scanning direction of the n-thscanning line is represented by Expression (34).

$\begin{matrix}{y = {n + \left( {B_{n} + {\sum\limits_{p = 1}^{n}A_{p}}} \right)}} & {{Expression}\mspace{14mu} (34)}\end{matrix}$

The value “y” on the left side of Expression (34) is defined only when“n” is an integer. That is, the value “y” is a discrete function.However, in the embodiment, each value “y” determined from an integer isinterpolated by linear interpolation and handled as a continuousfunction y=ft(n). In the embodiment, linear interpolation is used so asto simplify hardware, but interpolation of the function may be performedby other methods such as Lagrange interpolation and splineinterpolation.

When the pixel positions in the sub-scanning direction are denoted byy_(n0) and y_(n0+1) with respect to pixel numbers n0 and n0+1 in theembodiment, an expression of conversion into the continuous functionwithin a range of from the pixel position y_(n0) to the pixel positiony_(n0+1) in the sub-scanning direction is given below.

y=y _(n0)×(1−n+n0)+y _(n0+1)×(n−n0)  Expression (35)

The processing of FIG. 15 is performed once per scanning, that is, oncefor eight beams. Therefore, in Steps S7006 to S7008, the positionaldeviation amounts of the eight beams are collectively calculated, andall the calculated positional deviation amounts of the eight beams arestored in Step S7009. The processing in Steps S3705 to S3709 of FIG. 14is the same as that of FIG. 12 described in the first embodiment, andhence the description thereof is omitted.

According to the embodiment, even when the irradiation position of alaser is deviated from the ideal pixel position on the photosensitivedrum 102 due to the factors such as a fluctuation in rotation speed ofthe photosensitive drum 102 and the optical face tangle error of therotary polygon mirror 204, satisfactory image quality without colordeviation and banding can be obtained.

As described above, according to the embodiment, satisfactory imagequality can be obtained by correcting distortion and uneven imagedensity of an image.

Other Embodiments

In the above-mentioned embodiments, the processing of the presentinvention is applied to, particularly, the correction in thesub-scanning direction. However, the processing of the present inventioncan be similarly applied to the correction of distortion in otherdirections, e.g., the main scanning direction. Further, in the secondembodiment, the rotation speed data of the photosensitive drum 102 isobtained in real time from the rotary encoder 301 and fed back topositional deviation correction. However, a profile of speed fluctuationdata measured in advance may be stored in the memory 302, and correctionmay be made in accordance with the stored profile. Further, whenpositional deviation information is obtained in real time, thepositional deviation information may be directly used for correctionalthough control is delayed. In this case, in order to prevent theinfluence caused by the delayed control, a particular frequencycomponent such as a high-frequency component may be filtered withrespect to a fluctuation amount of positional deviation to be used forcorrection.

Further, besides the linear interpolation and bicubic interpolation usedas interpolation systems of the embodiment, interpolation in which awindow function of a desired size is applied to a Sinc function orinterpolation involving determining a convolution function in accordancewith intended filter characteristics may be performed. Further, thepresent invention can be applied to an image output system or an imageoutput device in which an interval between output pixels and lines isdistorted irrespective of whether the system is an LED exposure systemor an electrophotographic system. Further, in the embodiment,interpolation is performed by correcting a position of a pixel of aninput image in accordance with Expressions (17) and (18), but functionsapproximate to Expressions (17) and (18) may be selected to be used forcorrection depending on the intended correction accuracy. Further, theconfiguration using the CPU 303 as the controller is described, but anapplication specific integrated circuit (ASIC), for example, may beused.

As described above, according to the other embodiments, satisfactoryimage quality can be obtained by correcting distortion and uneven imagedensity of an image.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2015-141777, filed Jul. 16, 2015, which is hereby incorporated byreference herein in its entirety.

What is claimed is:
 1. A correction method for an image formingapparatus, the image forming apparatus comprising: a light sourcecomprising a plurality of light emitting points; a photosensitive memberconfigured to rotate in a first direction so that a latent image isformed on the photosensitive member with light beams emitted from thelight source; and a deflection unit configured to deflect the lightbeams emitted from the light source to move spots of the light beamsradiated to the photosensitive member in a second direction orthogonalto the first direction to form scanning lines, the correction methodcomprising: a storing step of storing, in a storage unit, information onpositional deviation of the scanning lines in the first direction; aconversion step of converting positions of pixels of an input image byperforming coordinate transformation based on the information stored inthe storage unit so that an interval between the scanning lines on thephotosensitive member becomes a predetermined interval; and a filteringstep of determining pixel values of pixels of an output image bysubjecting pixel values of the pixels of the input image to aconvolution operation based on the positions of the pixels of the inputimage after the coordinate transformation.
 2. A correction methodaccording to claim 1, wherein the conversion step comprises determiningthe positions of the pixels of the input image after the coordinatetransformation with use of an inverse function ft⁻¹(n) of a functionft(n) by the following expression:fs′(n)=ft′(ft ⁻¹(fs(n))) where: fs(n) represents a function indicating aposition of an n-th pixel in the first direction of the input image;ft(n) represents a function indicating a position of the n-th pixel inthe first direction of the output image; fs′(n) represents a functionindicating a position of the n-th pixel in the first direction of theinput image after the coordinate transformation; and ft′(n) represents afunction indicating a position of the n-th pixel in the first directionof the output image after the coordinate transformation.
 3. A correctionmethod according to claim 2, wherein the conversion step comprisesdetermining, when the function fs(n) satisfies fs(n)=n and the functionft′(n) satisfies ft′(n)=n, the positions of the pixels of the inputimage after the coordinate transformation by the following expression:fs′(n)=ft ⁻¹(n).
 4. A correction method according to claim 2, whereinthe conversion step comprises interpolating, when the function fs(n)indicating the positions of the pixels of the input image or thefunction ft(n) indicating the positions of the pixels of the outputimage takes discrete values, the discrete values to obtain a continuousfunction.
 5. A correction method according to claim 1, wherein thefiltering step comprises performing the convolution operation with useof linear interpolation or bicubic interpolation.
 6. A correction methodaccording to claim 1, wherein the pixel values comprise density values,and wherein the filtering step comprises storing density values perpredetermined area before and after performing the convolutionoperation.
 7. A correction method according to claim 2, wherein, in thefiltering step, when a width in the first direction within a rangeexcluding 0 of a convolution function to be used for the convolutionoperation is defined as 2L, a range of from ymin to ymax of the pixelsof the input image corresponding to a range of the width of 2L with aposition yn of a predetermined pixel of the output image being a centeris defined as the following expressions:ymin=ft(yn−L); andymax=ft(yn+L).
 8. A correction method according to claim 1, wherein theimage forming apparatus further comprises a detection unit configured todetect a rotation speed of the photosensitive member, and wherein thepositional deviation in the first direction is corrected based on therotation speed of the photosensitive member detected by the detectionunit.
 9. A correction method according to claim 1, wherein thedeflection unit comprises a rotary polygon mirror having a predeterminednumber of faces, and wherein the information to be stored in the storageunit contains information on a variation in angle for each of the faceswith respect to a rotary shaft of the rotary polygon mirror.
 10. Acorrection method according to claim 1, wherein the predeterminedinterval is determined in accordance with a resolution of imageformation by the image forming apparatus.